Equations Reducible to a Pair of Linear Equations in Two Variables

Q.

Solve the following pair of linear equations:
$\frac{2}{\sqrt{x}}+\frac{3}{\sqrt{y}}=2$
$\frac{4}{\sqrt{x}}-\frac{9}{\sqrt{y}}=-1$
(where $x>0,y>0)$

1. $x=9,y=4$

2. $x=4,y=9$

3. $x=3,y=2$

4. $x=\frac{1}{2},y=\frac{1}{3}$

Q. How the equation $\sqrt{x}=4$ can be made linear? (where $x\ge 0$)

1. Substitute $x=u^2$, now the equation is linear in variable $x$
2. Substitute $x=u^3$, now the equation is linear in variable u
3. Substitute $x=u^2$, now the equation is linear in variable u
4. Substitute $x=u^4$, now the equation is linear in variable u

Q.

Solve the following pair of equations.
$\frac{1}{x}+\frac{3}{y}=1$
$\frac{6}{x}-\frac{12}{y}=2$
(where $x\ne 0,y\ne 0)$

1. $x=\frac{3}{5},y=\frac{7}{3}$

2. $x=\frac{5}{3},y=\frac{15}{2}$

3. $x=3,y=11$

4. $x=4,y=9$

Q.

Solve the following pair of equations:
$\frac{5}{x-1}+\frac{1}{y-2}=2$
$\frac{6}{x-1}-\frac{3}{y-2}=1$
(where $x\ne 1,y\ne 2)$

1. $x=4$, $y=5$

2. $x=\frac{1}{3},y=\frac{1}{3}$

3. $x=5$, $y=4$

4. None of the above

Q. Solve the following pair of linear equations by the substitution method.
$$0.2x+0.3y=1.3;0.4x+0.5y=2.3$$

Q. Ankita travels 14 km to her home partly by rickshaw and partly by bus. She takes half an hour if she travels 2 km by rickshaw and the remaining distance by bus. On the other hand, if she travels 4 km by rickshaw and the remaining distance by bus, she takes 9 minutes longer. Find the speed of the rickshaw and the bus in km/hr respectively.

1. 10 km/hr, 40 km/hr
2. 30 km/hr, 10 km/hr
3. 10 km/hr, 30 km/hr
4. 40 km/hr, 10 km/hr

Q. How will you make the following equations linear?
$\frac{5}{x-1}+\frac{1}{y-2}=2$
$\frac{6}{x-1}+\frac{3}{y-2}=1$
(where $x\ne 1andy\ne 2)$

1. Substitute $\frac{1}{x-1}$ as p and $\frac{1}{y-2}$ as q
2. Substitute $x=X+1$ and $y=Y+2$
3. The equation is already linear
4. None of the above

Q.

Solve the following pair of equations.

$\frac{7x-2y}{xy}=5$

$\frac{8x+6y}{xy}=15$

Here, x $\ne$ 0 and y $\ne$ 0.

1. x = 2, y = -5

2. $x=\frac{5}{2},\text{y is not defined}$

3. $x=-\frac{2}{5},\text{y is not defined}$

4. $x=\frac{4}{3},y=\frac{7}{2}$

Q.

Is $\sqrt{x}=4$ linear equation? If not then how the equation can be made linear.

1. None of these

2. Yes

3. No, substitute x=u², now the equation is linear in variable x

4. No, substitute x=u², now the equation is linear in variable u

Q.

What will you substitute to make the following equation a linear equation

$\frac{1}{x}$ + $\frac{3}{y}$ = 1

1. None of the above

2. 1/x as p and 1/y as q

3. x as 1/p and y as 1/q

4. Any of the above